Should he marry a girl who insists on going out wearing adornment (tabarruj) even though her character is good?

Praise be to Allah.

Firstly: 

The Prophet (peace and blessings of Allaah be upon him) encouraged us to marry women who are religiously committed. He said: “Women may be married for four things: their wealth, their lineage, their beauty and their religious commitment. Choose the one who is religiously-committed, may your hands be rubbed with dust (i.e., may your prosper).” Narrated by al-Bukhaari, 5090; Muslim, 1466. 

And he (peace and blessings of Allaah be upon him) said: “This world is transient comforts, and the best of the comforts of this world is a righteous woman.” Narrated by Muslim, 1467. Whoever fails to find a righteous wife misses out on the best of the comforts of this world, one that is better than wealth, children and status, etc. 

This should motivate the Muslim to seek a wife who is religiously committed and of good character, and to give such a woman precedence over all others, and not to be heedless about the best of the comforts of this world. 

A righteous woman is the one who pays attention to the rights of Allaah and the rights of other people, and the person who has the greatest rights over her is her husband. 

Persisting in sin is worse than the sin itself, because it is indicative of weakness of faith and failure to respect Allaah, and it means that the person is careless about things that may be detrimental to his religious commitment. 

Secondly: 

As well as being an act of disobedience and sin, going out wearing one’s adornment is also indicative of a woman’s bad attitude and lack of modesty. How can a chaste and modest woman be content to have people look at her and enjoy her beauty? 

But because of her weakness of faith and the strength of her whims and desires, the woman who goes out wearing her adornment does not realize how bad her action is, as Allaah says (interpretation of the meaning):  

“and Shaytaan (Satan) made fair‑seeming to them that which they used to do”

[al-An’aam 6:43]

Many of those who used to go out wearing their adornment, when Allaah blesses them with guidance, become appalled at their former immodest ways. 

There are well known reports which warn against tabarruj (wanton display of one's beauty and adornments), such as the words of the Prophet (peace and blessings of Allaah be upon him): “There are two types of the people of Hell whom I have not seen: people with whips like the tails of cattle, with which they strike the people, and women who are clothed yet naked, walking with an enticing gait, with something on their heads that looks like the humps of camels, leaning to one side. They will never enter Paradise or even smell its fragrance, although its fragrance can be detected from such and such a distance.” Narrated by Muslim, 2128. 

And he (peace and blessings of Allaah be upon him) said: “Any woman who perfumes herself then passes by the people so that they can smell her fragrance is an adulteress.” Narrated by Abu Dawood, 4173; al-Tirmidhi, 2786; al-Nasaa’i, 5126; classed as hasan by al-Albaani in Saheeh al-Nasaa’i. 

If this sin is repeated, it creates a black spot on the heart, until the whole heart is blackened, as the Prophet (peace and blessings of Allaah be upon him) said: “If the believer commits a sin, a black spot appears on his heart. If he repents, gives it up and seeks forgiveness, his heart is cleansed, but if he does more then (that spot) increases until it covers his heart. That is the raan (covering of sin) which Allaah mentioned in the Qur’aan: 

“Nay! But on their hearts is the Raan (covering of sins and evil deeds) which they used to earn”

[al-Mutaffifeen 83:14]

Narrated by al-Tirmidhi, 3334; Ibn Maajah, 4244; classed as hasan by al-Albaani in Saheeh al-Tirmidhi. 

You should note that marriage to a woman who persists in going out wearing her adornment can only mean one of two things: 

1 – That the husband has given in to her, and is keeping quiet about her evil action, so he will carry a burden of major sin in the Hereafter and shame in this world, for he is a shepherd who is responsible for his flock. 

How can a wise man accept to walk with his wife in the street when she is showing her adornment, and the men around him are looking at her and enjoying the view?! 

2 – That he will stay with her in a state of conflict and fighting and disagreement. This may be a cause of distress and anguish which no wise man would accept. So err on the side of caution, for there is nothing like being on the safe side. Look for a wife who is religiously committed, for a righteous woman will be good for you, praise be to Allaah. A righteous woman is the best of the comforts of this world; she will help you to obey Allaah, remind you of what is right and proper, guard herself and her husband’s wealth, and raise righteous children for him who will worship Allaah. 

We ask Allaah to guide you and give you strength. 

And Allaah knows best.